Answer
Please see image
range = $\{-1,1,3,5,7,9\}$
Work Step by Step
$\left[\begin{array}{lll}
x & 2x+3 & (x,y)\\
\hline-2 & -4+3=-1 & (-2,-1)\\
-1 & -2+3=1 & (1,-1)\\
0 & 0+3=3 & (0,3)\\
1 & 2+3=5 & (1,5)\\
2 & 4+3=7 & (2,7)\\
3 & 6+3=9 & (3,9)
\end{array}\right]$
The range (second column values) is
$\{-1,1,3,5,7,9\}$